Estimating output equations using value data

Output equations are commonly used in macroeconomics. They have a leading role in explaining why some countries are rich or have large economies. The equations generally look like Y = f(K,L), meaning output depends on capital and labour. They are usually measured using financial values for output and capital.

The research paper here rejects a common interpretation of the equations when financial values are used in estimation. The argument, in my words, goes like this.

"It might be the case that output measured in physical goods is dependent on machines and physical goods used in production, as well as on labour. But the market value of the output, physical good inputs, and labour could be anything. For example, labour might have a great deal of market power and so be able to charge much more for their services than machine owners could. So the relation between output in physical goods and inputs in physical goods is not well measured by the estimation using values.

"What we do know is that total output is paid to capital and labour. This is an accounting equation, with little economic content. It accounts for the success of equations estimating the output equations; what they are measuring is the accounting identity in an approximate form. The estimated dependence of output on capital tells you little about how physical output varies with physical inputs, and a lot about how much those inputs are paid."

I have not worked out mathematically how people buying the goods would adjust their purchases of inputs faced with different market power of capital and labour suppliers. A non-precise argument is that they would tend to reduce the purchases of the expensive inputs, so the input prices would vary, and so as a result would their market values. Consequently, the equation estimation would be closer to the estimation of the effects on output of physical quantities. However, market values might not adjust perfectly to offset the change in prices - for example, a monopolist supplier of capital would likely see their income drop sharply if they sold part of their capital and broke up their monopoly. This loose argument suggests that the estimation of output equations gives the accounting identity but also partially the production equation.

Growth macroeconomists' research papers often include the assumption of perfect competition, which affects the relation between the physical and accounting equations. The implications of the above arguments are not generally used in analysis after estimations, although it would be a natural insertion into the "robustness section" that often occurs in empirical papers.

If you are interested in the previous arguments, one of the authors has a full directory of their research here, including alternative empirical estimates of the East Asian growth experience, which is helpful as criticism without a different empirical approach can be deflating.